A Fast and Effective Method for Pruning of Non-dominated Solutions in Many-Objective Problems

Kukkonen, Saku; Deb, Kalyanmoy

doi:10.1007/11844297_56

Cited by 95 publications

(62 citation statements)

References 12 publications

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“…In each iteration, each individual is compared with its evolved value in order to decide whether the individual needs to be replaced by its evolved value. For metaheuristics that treat the multiobjective optimization problem as whole [6][7][8][9][10][11][12][13][14][15][16], the comparison is based on Pareto dominance. As Pareto dominance is a partial order, an inappropriate selection of the value to stay in the population would negatively affect discovering the true Pareto front.…”

Section: Related Workmentioning

confidence: 99%

“…To obtain well distributed nondominated solutions on the Pareto front, metaheuristics need to promote the diversity of the elitists using techniques such as adaptive grid [12,13], clustering [14], crowding distance [6], fitness sharing [8], maximin sorting [15], vicinity distance [9,16], nearest neighbor density estimation [10], and weighted sum aggregation [22][23][24][25][26]. The weighted sum aggregation technique employed in the MOEA/D framework is the most efficient and assumes that the predefined uniformly distributed weight vectors result in reasonably distributed nondominated solutions; however, this assumption may be violated in cases where the Pareto front is discontinuous or has a shape of sharp peak and low tail [26].…”

Section: Related Workmentioning

confidence: 99%

“…Compared with traditional optimization methods such as linear programming, nonlinear programming, and optimal control theory, metaheuristics do not require characteristics such as continuity, differentiability, linearity, and convexity on the optimization problem; in addition, population-based metaheuristics can find multiple nondominated solutions in just one run for multiobjective optimization. Existing metaheuristics solve a multiobjective optimization problem by either treating the multiobjective problem as whole [6][7][8][9][10][11][12][13][14][15][16][17][18] or involving decomposition (i.e., decomposing the multiobjective problem into multiple single-objective problems) [1,[19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Multiswarm Comprehensive Learning Particle Swarm Optimization

Estevez

2018

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Multiswarm comprehensive learning particle swarm optimization (MSCLPSO) is a multiobjective metaheuristic recently proposed by the authors. MSCLPSO uses multiple swarms of particles and externally stores elitists that are nondominated solutions found so far. MSCLPSO can approximate the true Pareto front in one single run; however, it requires a large number of generations to converge, because each swarm only optimizes the associated objective and does not learn from any search experience outside the swarm. In this paper, we propose an adaptive particle velocity update strategy for MSCLPSO to improve the search efficiency. Based on whether the elitists are indifferent or complex on each dimension, each particle adaptively determines whether to just learn from some particle in the same swarm, or additionally from the difference of some pair of elitists for the velocity update on that dimension, trying to achieve a tradeoff between optimizing the associated objective and exploring diverse regions of the Pareto set. Experimental results on various two-objective and three-objective benchmark optimization problems with different dimensional complexity characteristics demonstrate that the adaptive particle velocity update strategy improves the search performance of MSCLPSO significantly and is able to help MSCLPSO locate the true Pareto front more quickly and obtain better distributed nondominated solutions over the entire Pareto front.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adaptive Multiswarm Comprehensive Learning Particle Swarm Optimization

Estevez

2018

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“…As the number of elitists quickly grows during the run, Rep has a fixed maximum size L max . Rep is maintained as follows in every generation: (1) A temporary set Tmp is initialized to be empty; (2) copy all the elitists in Rep to Tmp; (3) copy each particle's current position to Tmp; (4) apply mutation to some elitists randomly selected from Rep on a randomly selected dimension and add the mutated elitists to Tmp; (5) apply DE to a number of extreme and least crowded elitists in Rep on every dimension and add the differentially evolved elitists to Tmp; (6) remove any dominated individual from the solutions in Tmp; (7) sort the non-dominated solutions in Tmp using respectively the crowding distance technique [8] for 2-objective problems and the M-nearest-neighbors product-based vicinity distance technique [22] for problems with more than two objectives; (8) if the number of non-dominated solutions in Tmp is larger than L max , let the first L max solutions to stay in Tmp and remove the other solutions from Tmp; and (9) remove all the elitists in Rep and copy all the non-dominated solutions in Tmp to Rep. In Step (8), letting the non-dominated solutions with larger crowding/vicinity distances to stay helps to preserve the diversity of the resulting non-dominated solutions on the Pareto front.…”

Section: Optimization Framework Based Onmentioning

confidence: 99%

Multi-Objective Sustainable Operation of the Three Gorges Cascaded Hydropower System Using Multi-Swarm Comprehensive Learning Particle Swarm Optimization

Sun

Wang

et al. 2016

Energies

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Optimal operation of hydropower reservoir systems often needs to optimize multiple conflicting objectives simultaneously. The conflicting objectives result in a Pareto front, which is a set of non-dominated solutions. Non-dominated solutions cannot outperform each other on all the objectives. An optimization framework based on the multi-swarm comprehensive learning particle swarm optimization algorithm is proposed to solve the multi-objective operation of hydropower reservoir systems. Through adopting search techniques such as decomposition, mutation and differential evolution, the algorithm tries to derive multiple non-dominated solutions reasonably distributed over the true Pareto front in one single run, thereby facilitating determining the final tradeoff. The long-term sustainable planning of the Three Gorges cascaded hydropower system consisting of the Three Gorges Dam and Gezhouba Dam located on the Yangtze River in China is studied. Two conflicting objectives, i.e., maximizing hydropower generation and minimizing deviation from the outflow lower target to realize the system's economic, environmental and social benefits during the drought season, are optimized simultaneously. Experimental results demonstrate that the optimization framework helps to robustly derive multiple feasible non-dominated solutions with satisfactory convergence, diversity and extremity in one single run for the case studied.

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“…This is an expected result since DFCNT is a three-objective MOP, and it is well-known that the density estimator of SPEA2 overcomes those used in NSGA-II and PAES (used in the rest of algorithms) in MOPs having more than two objectives [17]. In this sense, it is remarkable the HV values reached by the ES algorithm, which outperforms NSGA-II, the reference algorithm in multiobjective optimization.…”

Section: Resultsmentioning

confidence: 56%

Metaheuristic Approaches for Optimal Broadcasting Design in Metropolitan MANETs

Alba

Cervantes

Gómez

et al.

Computer Aided Systems Theory – EUROCAST 2007

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Abstract. Mobile Ad-hoc Networks (MANETs) are composed of a set of communicating devices which are able to spontaneously interconnect without any pre-existing infrastructure. In such scenario, broadcasting becomes an operation of tremendous importance for the own existence and operation of the network. Optimizing a broadcasting strategy in MANETs is a multiobjective problem accounting for three goals: reaching as many stations as possible, minimizing the network utilization, and reducing the duration of the operation itself. This research, which has been developed within the OPLINK project (http://oplink.lcc.uma.es), faces a wide study about this problem in metropolitan MANETs with up to seven different advanced multiobjective metaheuristics. They all compute Pareto fronts of solutions which empower a human designer with the ability of choosing the preferred configuration for the network. The quality of these fronts is evaluated by using the hypervolume metric. The obtained results show that the SPEA2 algorithm is the most accurate metaheuristic for solving the broadcasting problem.

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A Fast and Effective Method for Pruning of Non-dominated Solutions in Many-Objective Problems

Cited by 95 publications

References 12 publications

Adaptive Multiswarm Comprehensive Learning Particle Swarm Optimization

Adaptive Multiswarm Comprehensive Learning Particle Swarm Optimization

Multi-Objective Sustainable Operation of the Three Gorges Cascaded Hydropower System Using Multi-Swarm Comprehensive Learning Particle Swarm Optimization

Metaheuristic Approaches for Optimal Broadcasting Design in Metropolitan MANETs

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